How do you get tranquillizer mode in rct3 platinum

The animals have to not be in the fencing area for you to use the tranquillizer.
Once they are out, click them and select the tranquillizer or go to the top part of the screen and click the tranquillizer button at the right part.
When you buy animals, you can place them outside the fencing. You can use the tranquillizer then to.